IS 



514 Sir J. J. Thomson on the Structure of 



as 1/<9 S 3 . If the electrons were arranged round a ring 1/0/ 

 would be proportional to n z , and if the electrons were on a 

 sphere it would vary as m where n is the number of the 

 electrons, in either case it increases much more rapidly than n ; 

 n however measures the rate of increase of the left-hand side 



of (1). Hence even if for small values of n, ^r^l) 



greater than is necessary for stability by a considerable 

 margin,, as n increases the value of this quantity required for 

 stability increases faster than the increase in the charge ; 

 irence the margin of stability must ultimately disappear and 

 the arrangement become unstable. I have worked out the 

 value E of the central charge required to make the equi- 

 librium stable for symmetrical distribution of varying 

 numbers of electrons when the force due to the central 



E / c\ 

 charge E is expressed by -s { 1 ) . This law of force changes 



from attraction to repulsion only once, i. e. when r=c, and is 

 thus, about the simplest of its type. It will probably 

 represent with considerable accuracy the law of force in the 

 neighbourhood of a position of equilibrium for a much more 

 general type of force. I hope to give the analysis in a 

 separate paper. I will here quote two results which I have 

 already given in lectures at the Royal Institution. The first 

 table gives the value of the ratio of E/e to make the equi- 

 librium of n electrons arranged at equal intervals round a 

 circular ring stable when the motion is confined to the plane 



of the ring. 









n= ] 



2 3 



4 5 



6 7 10 12 14 16 18 



E/e -70 



•75 1-58 



3-10 4-76 



7-32 14-2 24-48 38-9 58 83 115 



Thus to keep 10 electrons stable in a ring would require a 

 central charge at least 25 times that on a single electron, 

 while if there are more than 5 electrons in a ring the charge 

 at the centre must be greater than the sum of the charges on 

 -the electrons. 



The next table gives the value of E/e when the electrons 

 are arranged at the corners of a regular polyhedron instead 

 of at equal intervals round a ring in one plane. 



n= 1 2 3 4 6 8 12 20 



E/e.... -70 -75 i'58 2-44 4-8 7-6 13 30 



These results are independent of the value of c, the constant 

 .in the expression for the law of force. 



It may be pointed out that the cube is not the stable 



